Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Secret Teachings of All Ages
Pythagorean Mathematics (75)
The one was defined by the Platonists as "the summit of the many." The one differs from the monad in that the term monad is used to designate the sum of the parts considered as a unit, whereas the one is the term applied to each of its integral parts.
That the Intellectual Beings Are Not Outside the Intellectual-principle: and on the Nature of the Good (4)
We have said that all must be brought back to a unity: this must be an authentic unity, not belonging to the order in which multiplicity is unified...
(4) We have said that all must be brought back to a unity: this must be an authentic unity, not belonging to the order in which multiplicity is unified by participation in what is truly a One; we need a unity independent of participation, not a combination in which multiplicity holds an equal place: we have exhibited, also, the Intellectual Realm and the Intellectual-Principle as more closely a unity than the rest of things, so that there is nothing closer to The One. Yet even this is not The purely One.
This purely One, essentially a unity untouched by the multiple, this we now desire to penetrate if in any way we may.
Only by a leap can we reach to this One which is to be pure of all else, halting sharp in fear of slipping ever so little aside and impinging on the dual: for if we fail of the centre, we are in a duality which does not even include The authentic One but belongs on both sides, to the later order. The One does not bear to be numbered in with anything else, with a one or a two or any such quantity; it refuses to take number because it is measure and not the measured; it is no peer of other entities to be found among them; for thus, it and they alike would be included in some container and this would be its prior, the prior it cannot have. Not even essential number can belong to The One and certainly not the still later number applying to quantities; for essential number first appears as providing duration to the divine Intellection, while quantitative number is that which furnishes the Quantity found in conjunction with other things or which provides for Quantity independent of things, if this is to be thought of as number at all. The Principle which in objects having quantitative number looks to the unity from which they spring is a copy of the Principle which in the earlier order of number looks to the veritable One; and it attains its existence without in the least degree dissipating or shattering that prior unity: the dyad has come into being, but the precedent monad still stands; and this monad is quite distinct within the dyad from either of the two constituent unities, since there is nothing to make it one rather than the other: being neither, but simply that thing apart, it is present without being inherent.
But how are the two unities distinct and how is the dyad a unity, and is this unity the same as the unity by which each of the constituents is one thing?
Our answer must be that the unity is that of a participation in the primal unity with the participants remaining distinct from that in which they partake; the dyad, in so far as it is one thing, has this participation, but in a certain degree only; the unity of an army is not that of a single building; the dyad, as a thing of extension, is not strictly a unit either quantitatively or in manner of being.
Are we then to take it that the monads in the pentad and decad differ while the unity in the pentad is the same as that in the decad?
Yes, in the sense in which, big and little, ship is one with ship, army with army, city with city; otherwise, no. But certain difficulties in this matter will be dealt with later.
For there is no single existing being, which does not participate in the one, but as every number participates in an unit, and one dual and one decade...
(2) But One, because He is uniquely all, as beseems an excess of unique Oneness, and is Cause of all without departing from the One. For there is no single existing being, which does not participate in the one, but as every number participates in an unit, and one dual and one decade is spoken of, and one half, and one third and tenth, so everything, and part of everything participates in the one, and by the fact that the One is, all existing things are. And the Cause of all is not One, as one of many, but before every one and multitude, and determinative of every one and multitude. For there is no multitude which does not partake in some way or other of the one. Yea, that which is many by parts, is one in the whole; and the many by the accidents, is one by the subject; and the many by the number or the powers, is one by the species, and the many by the species, is one by the genus; and the many by the progressions, is one by the source. And there is no single thing which does not participate in some way in the one, which uniformly pre-held in the uniqueness throughout all, all and whole, all, even the things opposed. And indeed, without the one there will not be a multitude, but without the multitude there will be the one, even as the unit previous to every multiplied number; and, if any one should suppose, that all things are united to all, the All will be one in the whole.
As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule...
(15) As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule the hundredths; the hundredths rule the thousandths; the thousands rule the ten thousands. This is the pattern immortals. First Man is like this: His monad [...].
That the Intellectual Beings Are Not Outside the Intellectual-principle: and on the Nature of the Good (5)
We return to our statement that The First remains intact even when other entities spring from it. In the case of numbers, the unit remains intact...
(5) We return to our statement that The First remains intact even when other entities spring from it.
In the case of numbers, the unit remains intact while something else produces, and thus number arises in dependence on the unit: much more then does the unit, The One, remain intact in the principle which is before all beings; especially since the entities produced in its likeness, while it thus remains intact, owe their existence to no other, but to its own all-sufficient power.
And just as there is, primarily or secondarily, some form or idea from the monad in each of the successive numbers- the later still participating, though unequally, in the unit- so the series of Beings following upon The First bear, each, some form or idea derived from that source. In Number the participation establishes Quantity; in the realm of Being, the trace of The One establishes reality: existence is a trace of The One- our word for entity may probably be connected with that for unity.
What we know as Being, the first sequent upon The One, advanced a little outward, so to speak, then chose to go no further, turned inward again and comes to rest and is now the reality and hearth of the universe. Pressing on the word for Being we have the word "hen" , an indication that in our very form of speech we tell, as far as may be, that Being is that which proceeds from The One. Thus both the thing that comes to be and Being itself are carriers of a copy, since they are outflows from the power of The primal One: this power sees and in its emotion tries to represent what it sees and breaks into speech "On"; "einai"; "ousia," "hestia" , sounds which labour to express the essential nature of the universe produced by the travail of the utterer and so to represent, as far as sounds may, the origin of reality.
Now, no doubt, if these various activities are not themselves substantial existences- but merely manifestations of latent potentiality- there is no co...
(12) But why, after all, should it not be such a manifold as long as it remains one substantial existence, having the multiplicity not of a compound being but of a unity with a variety of activities?
Now, no doubt, if these various activities are not themselves substantial existences- but merely manifestations of latent potentiality- there is no compound; but, on the other hand, it remains incomplete until its substantial existence be expressed in act. If its substantial existence consists in its Act, and this Act constitutes multiplicity, then its substantial existence will be strictly proportioned to the extent of the multiplicity.
We allow this to be true for the Intellectual-Principle to which we have allotted self-knowing; but for the first principle of all, never. Before the manifold, there must be The One, that from which the manifold rises: in all numerical series, the unit is the first.
But- we will be answered- for number, well and good, since the suite makes a compound; but in the real beings why must there be a unit from which the multiplicity of entities shall proceed?
Because the multiplicity would consist of disjointed items, each starting at its own distinct place and moving accidentally to serve to a total.
But, they will tell us, the Activities in question do proceed from a unity, from the Intellectual-Principle, a simplex.
By that they admit the existence of a simplex prior to the Activities; and they make the Activities perdurable and class them as substantial existences ; but as Hypostases they will be distinct from their source, which will remain simplex; while its product will in its own nature be manifold and dependent upon it.
Now if these activities arise from some unexplained first activity in that principle, then it too contains the manifold: if, on the contrary, they are the very earliest activities and the source and cause of any multiple product and the means by which that Principle is able, before any activity occurs, to remain self-centred, then they are allocated to the product of which they are the cause; for this principle is one thing, the activities going forth from it are another, since it is not, itself, in act. If this be not so, the first act cannot be the Intellectual-Principle: the One does not provide for the existence of an Intellectual-Principle which thereupon appears; that provision would be something intervening between the One and the Intellectual-Principle, its offspring. There could, in fact, be no such providing in The One, for it was never incomplete; and such provision could name nothing that ought to be provided. It cannot be thought to possess only some part of its content, and not the whole; nor did anything exist to which it could turn in desire. Clearly anything that comes into being after it, arises without shaking to its permanence in its own habit. It is essential to the existence of any new entity that the First remain in self-gathered repose throughout: otherwise, it moved before there was motion and had intellectual act before any intellection- unless, indeed, that first act was incomplete, nothing more than a tendency. And what can we imagine it lights upon to become the object of such a tendency?
The only reasonable explanation of act flowing from it lies in the analogy of light from a sun. The entire intellectual order may be figured as a kind of light with the One in repose at its summit as its King: but this manifestation is not cast out from it: we may think, rather, of the One as a light before the light, an eternal irradiation resting upon the Intellectual Realm; this, not identical with its source, is yet not severed from it nor of so remote a nature as to be less than Real-Being; it is no blind thing, but is seeing and knowing, the primal knower.
The One, as transcending Intellect, transcends knowing: above all need, it is above the need of the knowing which pertains solely to the Secondary Nature. Knowing is a unitary thing, but defined: the first is One, but undefined: a defined One would not be the One-absolute: the absolute is prior to the definite.
In all forms, phases, and schools of philosophy we find this insistence upon the presence and existence of a One Something of which all else are but...
(8) In all forms, phases, and schools of philosophy we find this insistence upon the presence and existence of a One Something of which all else are but manifestations. In fact, as the wisest philosophers have informed us, the whole purpose of philosophy is to discover the One Unconditioned Ground of all that exists Conditionally. All philosophy worthy of the name is Monistic in essence. A leading authority on the history of philosophy informs us the: "Monism is, in strictness, a name applicable to any system of thought which sees in the universe the manifestation or working of a single principle. Such a unity may be at once the tacit presupposition and the goal of all philosophic effect, and in so far as a philosophy fails to harmonize the apparently independent and even conflicting facts of experience, as aspects or elements within a larger whole, it must be held to fall short of the necessary ideal of thought. Dualism, in an ultimate metaphysical reference, is a confession of the failure of philosophy to achieve its proper task; and this is a justification of those who consistently use the word as a term of reproach." And, now, let us take a brief passing glance at the Rosicrucian teachings concerning the manner in which the One proceeded to become the Many—the Unity to become Diversity—the Identical to become Variety—and yet remain the One, Unity, Identity of the World Soul, unaffected and unchanged by its plunge into Manifestation. Evolution we see on all sides around us, but all Evolution must be preceded by Involution, as all occultists and scientists know full well.
How then can a multitude of essential beings be really one? Obviously either the one essence will be entire in all, or the many will rise from a one...
(5) How then can a multitude of essential beings be really one?
Obviously either the one essence will be entire in all, or the many will rise from a one which remains unaltered and yet includes the one- many in virtue of giving itself, without self-abandonment, to its own multiplication.
It is competent thus to give and remain, because while it penetrates all things it can never itself be sundered: this is an identity in variety.
There is no reason for dismissing this explanation: we may think of a science with its constituents standing as one total, the source of all those various elements: again, there is the seed, a whole, producing those new parts in which it comes to its division; each of the new growths is a whole while the whole remains undiminished: only the material element is under the mode of part, and all the multiplicity remains an entire identity still.
It may be objected that in the case of science the constituents are not each the whole.
But even in the science, while the constituent selected for handling to meet a particular need is present actually and takes the lead, still all the other constituents accompany it in a potential presence, so that the whole is in every part: only in this sense is the whole science distinguished from the part: all, we may say, is here simultaneously effected: each part is at your disposal as you choose to take it; the part invites the immediate interest, but its value consists in its approach to the whole.
The detail cannot be considered as something separate from the entire body of speculation: so treated it would have no technical or scientific value; it would be childish divagation. The one detail, when it is a matter of science, potentially includes all. Grasping one such constituent of his science, the expert deduces the rest by force of sequence.
the geometrician, in his analysis, shows that the single proposition includes all the items that go to constitute it and all the propositions which can be developed from it.
It is our feebleness that leads to doubt in these matters; the body obscures the truth, but There all stands out clear and separate.
It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real...
(11) It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real existence why not the rest? We are certainly not compelled to attach that one henad to some one thing and so deprive all the rest of the means to unity: since every existent must be one thing, the unity is obviously common to all. This means one principle applying to many, the principle whose existence within itself we affirmed to be presupposed by its manifestation outside.
But if a henad exists in some given object and further is observed in something else, then that first henad being real, there cannot be only one henad in existence; there must be a multiplicity of henads.
Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads . If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity.
Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well?
Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously- or rather has produced once for all- not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent- not in the sense of moving from point to point but in its inner changes- it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason.
Especially must this be known, that according to the pre-conceived species of each one, things united are said to be made one, and the one is...
(3) Especially must this be known, that according to the pre-conceived species of each one, things united are said to be made one, and the one is elemental of all; and if you should take away the one, there will be neither totality nor part, nor any other single existing thing. For the one, uniformly, pre-held and comprehended all things in itself. For this reason, then, the Word of God celebrates the whole Godhead, as Cause of all, by the epithet of the One, both one God the Father, and one Lord Jesus Christ, and one and the same Spirit, by reason of the surpassing indivisibility of the whole Divine Oneness, in which all things are uniquely collected, and are super-unified, and are with It Superessentially. Wherefore also, all things are justly referred and attributed to It, by Which and from Which, and through Which, and in Which, and to Which, all things are, and are co-ordinated, and abide, and are held together, and are filled, and are turned towards It. And you would not find any existing thing, which is not what it is, and perfected and preserved, by the One, after which the whole Deity is superessentially named. And it is necessary also, that we being turned from the many to the One, by the power of the Divine Oneness, should celebrate as One the whole and one Deity--the one Cause of all--which is before every one and multitude, and part and whole, and limit and illimitability, and term and infinity, which bounds all things that be, even the Being Itself, and is uniquely Cause of all, individually and collectively, and at the same time before all, and above all, and above the One existing Itself, and bounding the One existing Itself; since the One existing--that in things being--is numbered, and number participates in essence; but the superessential One bounds both the One existing, and every number, and Itself is, of both one and number, and every being, Source and Cause, and Number and. Order. Wherefore also, whilst celebrated as Unit and Triad, the Deity above all is neither Unit nor Triad, as understood by us or by any other sort of being, but, in order that we may celebrate truly. Its super-oneness, and Divine generation, by the threefold and single name of God, we name the Deity, Which is inexpressible to things that be, the Superessential. But no Unit nor Triad, nor number nor unity, nor productiveness, nor any other existing thing, or thing known to any existing thing, brings forth the hiddenness, above every expression and every mind, of the Super-Deity Which is above all superessentially. Nor has It a Name, or expression, but is elevated above in the inaccessible. And neither do we apply the very Name of Goodness, as making it adequate to It, but through a desire of understanding and saying something concerning that inexpressible nature, we consecrate the most august of Names to It, in the first degree, and although we should be in accord in this matter with the theologians, yet we shall fall short of the truth of the facts. Wherefore, even they have given the preference to the ascent through negations, as lifting the soul out of things kindred to itself, and conducting it through all the Divine conceptions, above which towers that which is above every name, and every expression and knowledge, and at the furthest extremity attaching it to Him, as far indeed as is possible for us to be attached to that Being.
The Origin and Order of the Beings. Following on the First (1)
The One is all things and no one of them; the source of all things is not all things; all things are its possession- running back, so to speak, to...
(1) The One is all things and no one of them; the source of all things is not all things; all things are its possession- running back, so to speak, to it- or, more correctly, not yet so, they will be.
But a universe from an unbroken unity, in which there appears no diversity, not even duality?
It is precisely because that is nothing within the One that all things are from it: in order that Being may be brought about, the source must be no Being but Being's generator, in what is to be thought of as the primal act of generation. Seeking nothing, possessing nothing, lacking nothing, the One is perfect and, in our metaphor, has overflowed, and its exuberance has produced the new: this product has turned again to its begetter and been filled and has become its contemplator and so an Intellectual-Principle.
That station towards the one establishes Being; that vision directed upon the One establishes the Intellectual-Principle; standing towards the One to the end of vision, it is simultaneously Intellectual-Principle and Being; and, attaining resemblance in virtue of this vision, it repeats the act of the One in pouring forth a vast power.
This second outflow is a Form or Idea representing the Divine Intellect as the Divine Intellect represented its own prior, The One.
This active power sprung from essence is Soul.
Soul arises as the idea and act of the motionless Intellectual-Principle- which itself sprang from its own motionless prior- but the soul's operation is not similarly motionless; its image is generated from its movement. It takes fulness by looking to its source; but it generates its image by adopting another, a downward, movement.
This image of Soul is Sense and Nature, the vegetal principle.
Nothing, however, is completely severed from its prior. Thus the human Soul appears to reach away as far down as to the vegetal order: in some sense it does, since the life of growing things is within its province; but it is not present entire; when it has reached the vegetal order it is there in the sense that having moved thus far downwards it produces- by its outgoing and its tendency towards the less good- another hypostasis or form of being just as its prior (the loftier phase of the Soul) is produced from the Intellectual-Principle which yet remains in untroubled self-possession.
In what sense, then, do we assert this Unity, and how is it to be adjusted to our mental processes? Its oneness must not be entitled to that of monad...
(6) In what sense, then, do we assert this Unity, and how is it to be adjusted to our mental processes?
Its oneness must not be entitled to that of monad and point: for these the mind abstracts extension and numerical quantity and rests upon the very minutest possible, ending no doubt in the partless but still in something that began as a partible and is always lodged in something other than itself. The Unity was never in any other and never belonged to the partible: nor is its impartibility that of extreme minuteness; on the contrary it is great beyond anything, great not in extension but in power, sizeless by its very greatness as even its immediate sequents are impartible not in mass but in might. We must therefore take the Unity as infinite not in measureless extension or numerable quantity but in fathomless depths of power.
Think of The One as Mind or as God, you think too meanly; use all the resources of understanding to conceive this Unity and, again, it is more authentically one than God, even though you reach for God's unity beyond the unity the most perfect you can conceive. For This is utterly a self-existent, with no concomitant whatever. This self-sufficing is the essence of its unity. Something there must be supremely adequate, autonomous, all-transcending, most utterly without need.
Any manifold, anything beneath The Unity, is dependent; combined from various constituents, its essential nature goes in need of unity; but unity cannot need itself; it stands unity accomplished. Again, a manifold depends upon all its factors; and furthermore each of those factors in turn- as necessarily inbound with the rest and not self-standing- sets up a similar need both to its associates and to the total so constituted.
The sovranly self-sufficing principle will be Unity-Absolute, for only in this Unity is there a nature above all need, whether within itself or in regard to the rest of things. Unity seeks nothing towards its being or its well-being or its safehold upon existence; cause to all, how can it acquire its character outside of itself or know any good outside? The good of its being can be no borrowing: This is The Good. Nor has it station; it needs no standing ground as if inadequate to its own sustaining; what calls for such underpropping is the soulless, some material mass that must be based or fall. This is base to all, cause of universal existence and of ordered station. All that demands place is in need; a First cannot go in need of its sequents: all need is effort towards a first principle; the First, principle to all, must be utterly without need. If the Unity be seeking, it must inevitably be seeking to be something other than itself; it is seeking its own destroyer. Whatever may be said to be in need of a good is needing a preserver; nothing can be a good to The Unity, therefore.
Neither can it have will to anything; it is a Beyond-Good, not even to itself a good but to such beings only as may be of quality to have part with it. Nor has it Intellection; that would comport diversity: nor Movement; it is prior to Movement as to Intellection.
To what could its Intellection be directed? To itself? But that would imply a previous ignorance; it would be dependent upon that Intellection in order to knowledge of itself; but it is the self-sufficing. Yet this absence of self-knowing does not comport ignorance; ignorance is of something outside- a knower ignorant of a knowable- but in the Solitary there is neither knowing nor anything unknown. Unity, self-present, it has no need of self-intellection: indeed this "self-presence" were better left out, the more surely to preserve the unity; we must eliminate all knowing and all association, all intellection whether internal or external. It is not to be though of as having but as being Intellection; Intellection does not itself perform the intellective act but is the cause of the act in something else, and cause is not to be identified with caused: most assuredly the cause of all is not a thing within that all.
This Principle is not, therefore, to be identified with the good of which it is the source; it is good in the unique mode of being The Good above all that is good.
As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the...
(5) As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the divine, unless by a deliberate apostasy.
Bringing itself close to the divine Intellect, becoming, as it were, one with this, it seeks still further: What Being, now, has engendered this God, what is the Simplex preceding this multiple; what the cause at once of its existence and of its existing as a manifold; what the source of this Number, this Quantity?
Number, Quantity, is not primal: obviously before even duality, there must stand the unity.
The Dyad is a secondary; deriving from unity, it finds in unity the determinant needed by its native indetermination: once there is any determination, there is Number, in the sense, of course, of the real Number. And the soul is such a number or quantity. For the Primals are not masses or magnitudes; all of that gross order is later, real only to the sense-thought; even in seed the effective reality is not the moist substance but the unseen- that is to say Number and the Reason-Principle .
Thus by what we call the Number and the Dyad of that higher realm, we mean Reason Principles and the Intellectual-Principle: but while the Dyad is, as regards that sphere, undetermined- representing, as it were, the underly of The One- the later Number - that which rises from the Dyad and The One- is not Matter to the later existents but is their forming-Idea, for all of them take shape, so to speak, from the ideas rising within this. The determination of the Dyad is brought about partly from its object- The One- and partly from itself, as is the case with all vision in the act of sight: intellection is vision occupied upon The One.
Anaxagoras, again, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in...
(9) Anaxagoras, again, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision.
Heraclitus, with his sense of bodily forms as things of ceaseless process and passage, knows the One as eternal and intellectual.
In Empedocles, similarly, we have a dividing principle, "Strife," set against "Friendship"- which is The One and is to him bodiless, while the elements represent Matter.
Later there is Aristotle; he begins by making the First transcendent and intellective but cancels that primacy by supposing it to have self-intellection. Further he affirms a multitude of other intellective beings- as many indeed as there are orbs in the heavens; one such principle as in- over to every orb- and thus his account of the Intellectual Realm differs from Plato's and, failing reason, he brings in necessity; though whatever reasons he had alleged there would always have been the objection that it would be more reasonable that all the spheres, as contributory to one system, should look to a unity, to the First.
We are obliged also to ask whether to Aristotle's mind all Intellectual Beings spring from one, and that one their First; or whether the Principles in the Intellectual are many.
If from one, then clearly the Intellectual system will be analogous to that of the universe of sense-sphere encircling sphere, with one, the outermost, dominating all- the First will envelop the entire scheme and will be an Intellectual Kosmos; and as in our universe the spheres are not empty but the first sphere is thick with stars and none without them, so, in the Intellectual Kosmos, those principles of Movement will envelop a multitude of Beings, and that world will be the realm of the greater reality.
If on the contrary each is a principle, then the effective powers become a matter of chance; under what compulsion are they to hold together and act with one mind towards that work of unity, the harmony of the entire heavenly system? Again what can make it necessary that the material bodies of the heavenly system be equal in number to the Intellectual moving principles, and how can these incorporeal Beings be numerically many when there is no Matter to serve as the basis of difference?
For these reasons the ancient philosophers that ranged themselves most closely to the school of Pythagoras and of his later followers and to that of Pherekudes, have insisted upon this Nature, some developing the subject in their writings while others treated of it merely in unwritten discourses, some no doubt ignoring it entirely.
It remains then to consider whether Being by its distinction produced Number or Number produced that distinction. It is certain that either Number...
(9) It remains then to consider whether Being by its distinction produced Number or Number produced that distinction. It is certain that either Number was the cause of Being, movement, rest, identity and difference, or these the cause of Number.
The first question is whether Number can exist in and of itself or is dependent upon things- Two being something observed in two things, Three in three; and so of the arithmetical One, for if this could exist apart from numbered objects it could exist also before the divisions of Being.
But could it precede Being itself?
For the present we must take it that Being precedes Number, is its source. But if One means one being and the duality two beings, then unity precedes Being, and Number precedes the Beings.
Mentally, to our approach? Yes: and in reality of existence as well.
Let us consider: When we think of the existence and the fine appearance of a man as forming one thing, that unity is certainly thought of as subsequent to a precedent duality; when we group a horse with a dog, the duality is obviously the subsequent. But think of that which brings man or horse or dog into being or produces them, with full intention, from where they lie latent within itself: the producer must say "I begin with a first, I pass on to a second; that makes two; counting myself there are three." Of course there was no such numbering even of Beings for their production, since the due number was known from the very beginning; but this consideration serves to show that all Number precedes the very Beings themselves.
But if Number thus preceded the Beings, then it is not included among them?
The truth is that it existed within the Authentic Being but not as applying to it, for Being was still unparted; the potentiality of Number existed and so produced the division within Being, put in travail with multiplicity; Number must be either the substance of Being or its Activity; the Life-Form as such and the Intellectual-Principle must be Number. Clearly Being is to be, thought of as Number Collective, while the Beings are Number unfolded: the Intellectual-Principle is Number moving within itself, while the Living-Form is Number container of the universe. Even Being is the outcome of the Unity, and, since the prior is unity, the secondary must be Number.
Hence it is that the Forms have been described as Henads and Numbers. This is the authentic Number; the other, the "monadic" is its image. The Authentic is that made manifest in the Forms and helping to bring them to be; primally it is the Number in the Authentic Being, inherent to it and preceding the Beings, serving to them as root, fount, first principle.
For the Unity is source to Being; Being's Being is stayed upon the Unity as its safeguard from dissolution; the Unity cannot rest upon Being which at that would be a unity before possessing unity; and so with the decad before possessing decadhood.
Chapter XII: God Cannot Be Embraced in Words or By the Mind. (9)
And therefore it is without form and name.
(9) For the One is indivisible; wherefore also it is infinite, not considered with reference to inscrutability, but with reference to its being without dimensions, and not having a limit. And therefore it is without form and name.
We may be told that unity and monad have no real existence, that the only unity is some definite object that is one thing, so that all comes to an...
(12) We may be told that unity and monad have no real existence, that the only unity is some definite object that is one thing, so that all comes to an attitude of the mind towards things considered singly.
But, to begin with, why at this should not the affirmation of Being pass equally as an attitude of mind so that Being too must disappear? No doubt Being strikes and stings and gives the impression of reality; but we find ourselves just as vividly struck and impressed in the presence of unity. Besides, is this attitude, this concept itself, a unity or a manifold? When we deny the unity of an object, clearly the unity mentioned is not supplied by the object, since we are saying it has none; the unity therefore is within ourselves, something latent in our minds independently of any concrete one thing.
"But the unity we thus possess comes by our acceptance of a certain idea or impression from things external; it is a notion derived from an object. Those that take the notion of numbers and of unity to be but one species of the notions held to be inherent in the mind must allow to numbers and to unity the reality they ascribe to any of the others, and upon occasion they must be met; but no such real existence can be posited when the concept is taken to be an attitude or notion rising in us as a by-product of the objects; this happens when we say "This," "What," and still more obviously in the affirmations "Crowd," "Festival," "Army," "Multiplicity." As multiplicity is nothing apart from certain constituent items and the festival nothing apart from the people gathered happily at the rites, so when we affirm unity we are not thinking of some Oneness self-standing, unrelated. And there are many other such cases; for instance "on the right," "Above" and their opposites; what is there of reality about this "On-the-right-ness" but the fact that two different positions are occupied? So with "Above": "Above" and "Below" are a mere matter of position and have no significance outside of this sphere.
Now in answer to this series of objections our first remark is that there does exist an actuality implicit in each one of the relations cited; though this is not the same for all or the same for correlatives or the same for every reference to unity.
It may be suggested that, while in the unities of the partial order the essence and the unity are distinct, yet in collective existence, in Real...
(2) It may be suggested that, while in the unities of the partial order the essence and the unity are distinct, yet in collective existence, in Real Being, they are identical, so that when we have grasped Being we hold unity; Real Being would coincide with Unity. Thus, taking the Intellectual-Principle as Essential Being, that principle and the Unity Absolute would be at once Primal Being and Pure Unity, purveying, accordingly, to the rest of things something of Being and something, in proportion, of the unity which is itself.
There is nothing with which the unity would be more plausibly identified than with Being; either it is Being as a given man is man or it will correspond to the Number which rules in the realm of the particular; it will be a number applying to a certain unique thing as the number two applies to others.
Now if Number is a thing among things, then clearly so this unity must be; we would have to discover what thing of things it is. If Number is not a thing but an operation of the mind moving out to reckon, then the unity will not be a thing.
We found that anything losing unity loses its being; we are therefore obliged to enquire whether the unity in particulars is identical with the being, and unity absolute identical with collective being.
Now the being of the particular is a manifold; unity cannot be a manifold; there must therefore be a distinction between Being and Unity. Thus a man is at once a reasoning living being and a total of parts; his variety is held together by his unity; man therefore and unity are different- man a thing of parts against unity partless. Much more must Collective Being, as container of all existence, be a manifold and therefore distinct from the unity in which it is but participant.
Again, Collective Being contains life and intelligence- it is no dead thing- and so, once more, is a manifold.
If Being is identical with Intellectual-Principle, even at that it is a manifold; all the more so when count is taken of the Ideal Forms in it; for the Idea, particular or collective, is, after all, a numerable agglomeration whose unity is that of a kosmos.
Above all, unity is The First: but Intellectual-Principle, Ideas and Being, cannot be so; for any member of the realm of Forms is an aggregation, a compound, and therefore- since components must precede their compound- is a later.
Other considerations also go to show that the Intellectual-Principle cannot be the First. Intellect must be above the Intellectual Act: at least in its higher phase, that not concerned with the outer universe, it must be intent upon its Prior; its introversion is a conversion upon the Principle.
Considered as at once Thinker and Object of its Thought, it is dual, not simplex, not The Unity: considered as looking beyond itself, it must look to a better, to a prior: looking simultaneously upon itself and upon its Transcendent, it is, once more, not a First.
There is no other way of stating Intellectual-Principle than as that which, holding itself in the presence of The Good and First and looking towards That, is self-present also, self-knowing and Knowing itself as All-Being: thus manifold, it is far from being The Unity.
In sum: The Unity cannot be the total of beings, for so its oneness is annulled; it cannot be the Intellectual-Principle, for so it would be that total which the Intellectual-Principle is; nor is it Being, for Being is the manifold of things.
To the argument touching relation we have an answer surely legitimate: The Unity is not of a nature to lose its own manner of being only because...
(14) To the argument touching relation we have an answer surely legitimate:
The Unity is not of a nature to lose its own manner of being only because something else stands in a state which it does not itself share; to stray from its unity it must itself suffer division into duality or the still wider plurality.
If by division the one identical mass can become a duality without loss of quantity, clearly the unity it possessed and by this destructive division lost was something distinct. What may be alternatively present and absent to the same subject must be classed among Real-Beings, regardless of position; an accidental elsewhere, it must have reality in itself whether it be manifested in things of sense or in the Intellectual- an accidental in the Laters but self-existent in the higher, especially in the First in its aspect of Unity developing into Being. We may be told that Unity may lose that character without change in itself, becoming duality by association with something else; but this is not true; unity does not become two things; neither the added nor what takes the addition becomes two; each remains the one thing it was; the duality is predicable of the group only, the unity remaining unchanged in each of those unchanged constituents.
Two and the Dyad are not essentially relative: if the only condition to the construction of duality were meeting and association such a relation might perhaps constitute Twoness and Duality; but in fact we see Duality produced by the very opposite process, by the splitting apart of a unity. This shows that duality- or any other such numerical form- is no relation produced either by scission or association. If one configuration produces a certain thing it is impossible that the opposite should produce the same so that the thing may be identified with the relation.
What then is the actual cause?
Unity is due to the presence of Unity; duality to that of Duality; it is precisely as things are white by Whiteness, just by Justice, beautiful by Beauty. Otherwise we must reject these universals and call in relation here also: justice would arise from a certain attitude in a given situation, Beauty from a certain pattern of the person with nothing present able to produce the beauty, nothing coming from without to effect that agreeable appearance.
You see something which you pronounce to be a unity; that thing possesses also size, form, and a host of other characteristics you might name; size, bulk, sweetness, bitterness and other Ideas are actually present in the thing; it surely cannot be thought that, while every conceivable quality has Real-Being, quantity has not and that while continuous quantity exists, discrete quantity does not and this though continuous quantity is measured by the discrete. No: as size by the presence of Magnitude, and Oneness by the presence of Unity, so with Duality and all the other numerical modes.
As to the How of participation, the enquiry is that of all participation in Ideal Forms; we must note, however, that the presence of the Decad in the looser totals is different from its presence in the continuous; there is difference again in its presence within many powers where multiplicity is concentred in unity; arrived at the Intellectuals, there too we discover Number, the Authentic Number, no longer entering the alien, Decad-Absolute not Decad of some particular Intellectual group.
On the Integral Omnipresence of the Authentic Existent (2) (6)
The Intellectual Beings, thus, are multiple and one; in virtue of their infinite nature their unity is a multiplicity, many in one and one over many,...
(6) The Intellectual Beings, thus, are multiple and one; in virtue of their infinite nature their unity is a multiplicity, many in one and one over many, a unit-plurality. They act as entire upon entire; even upon the partial thing they act as entire; but there is the difference that at first the partial accepts this working only partially though the entire enters later. Thus, when Man enters into human form there exists a particular man who, however, is still Man. From the one thing Man- man in the Idea- material man has come to constitute many individual men: the one identical thing is present in multiplicity, in multi-impression, so to speak, from the one seal.
This does not mean that Man Absolute, or any Absolute, or the Universe in the sense of a Whole, is absorbed by multiplicity; on the contrary, the multiplicity is absorbed by the Absolute, or rather is bound up with it. There is a difference between the mode in which a colour may be absorbed by a substance entire and that in which the soul of the individual is identically present in every part of the body: it is in this latter mode that Being is omnipresent.
That the Intellectual Beings Are Not Outside the Intellectual-principle: and on the Nature of the Good (6)
All this, however, we may leave to individual judgement: to proceed: This produced reality is an Ideal form- for certainly nothing springing from the...
(6) All this, however, we may leave to individual judgement: to proceed:
This produced reality is an Ideal form- for certainly nothing springing from the Supreme can be less- and it is not a particular form but the form of all, beside which there is no other; it follows that The First must be without form, and, if without form, then it is no Being; Being must have some definition and therefore be limited; but the First cannot be thought of as having definition and limit, for thus it would be not the Source but the particular item indicated by the definition assigned to it. If all things belong to the produced, which of them can be thought of as the Supreme? Not included among them, this can be described only as transcending them: but they are Being and the Beings; it therefore transcends Being.
Note that the phrase transcending Being assigns no character, makes no assertion, allots no name, carries only the denial of particular being; and in this there is no attempt to circumscribe it: to seek to throw a line about that illimitable Nature would be folly, and anyone thinking to do so cuts himself off from any slightest and most momentary approach to its least vestige.
As one wishing to contemplate the Intellectual Nature will lay aside all the representations of sense and so may see what transcends the sense-realm, in the same way one wishing to contemplate what transcends the Intellectual attains by putting away all that is of the intellect, taught by the intellect, no doubt, that the Transcendent exists but never seeking to define it.
Its definition, in fact, could be only "the indefinable": what is not a thing is not some definite thing. We are in agony for a true expression; we are talking of the untellable; we name, only to indicate for our own use as best we may. And this name, The One, contains really no more than the negation of plurality: under the same pressure the Pythagoreans found their indication in the symbol "Apollo" with its repudiation of the multiple. If we are led to think positively of The One, name and thing, there would be more truth in silence: the designation, a mere aid to enquiry, was never intended for more than a preliminary affirmation of absolute simplicity to be followed by the rejection of even that statement: it was the best that offered, but remains inadequate to express the Nature indicated. For this is a principle not to be conveyed by any sound; it cannot be known on any hearing but, if at all, by vision; and to hope in that vision to see a form is to fail of even that.